Global economic development trends

Walde’s criterion. It is recommended to use the maxim in strategy. It is found the condition and coincides with the lower price of the game . The value of , the guaranteed payoff that the first player can secure, is called the price of the game (the maxi min). The criterion is pessimistic, it is believed that nature will act in the worst way for a person.

Similarly, to determine the best strategy for the second player, we find the maximum payoff values by columns and, choosing the minimum value from them, we get:


where is the upper price of the game (minimax).
If the second player sticks to his minimax strategy. Then he is guaranteed to lose no more than .
3. Maximum criterion. The strategy is selected from the condition. The criterion is optimistic, it is believed that nature will be the most favorable for humans.
4. Hurwitz criterion. The recommended strategy is determined by the formula

Where is the degree of optimism, changing in the range .
The criterion takes into account the possibility of both the worst and the best behavior of nature. At , the criterion turns into. The Walde criterion. At , to the maximum criterion. A is influenced by the degree of responsibility of the decision maker in choosing the strategy. The grater the consequences of erroneous decisions, the greater the desire to insure, the closer a is to one.
Savage’s criterion. The essence of the criterion is to choose a strategy that does not allow excessively high losses. A risk matrix is found, the elements of which show what kind of kill a person will suffer if he does not choose the best strategy for each state of nature. The elements of the risk matrix are found by the formula

Where is the maximum element in a column of the original matrix.
The optimal strategy is fund from the expression